Using numerical methods to solve problems

**Question One.**

Use an appropriate method to find the root of *x*³ + *x * + 1 = 0 correct to 2 decimal places. Start with initial interval -0.8 and -0.6. Show all working.

**Question Two.**

Human blood pressure *P * (in mm of mercury) varies periodically with time (*t * in seconds). The first time during the first second of a cycle when the pressure *P* is 90 mm can be expressed by:

80 + 300*t* - 2700*t*³ = 90

or:

*f*(*t*) = 2700*t*³ - 300*t* + 10 = 0

Take an initial value of *t* = 0.05 seconds and use a method different to Question One to find a solution to *f*(*t*) = 0 accurate to 4 decimal places.